9. The necessary illumination for reading is about 2 foot-candles. How far away may an 8-candle-power lamp be placed?
10. What is the illumination in foot-candles upon a surface 20 ft. from an arc lamp having an intensity of 1000 candle power?
11. How far from a 100-candle-power Welsbach light would the illumination be 2 foot-candles?
(3) Mirrors and the Formation of Images
Fig. 353.—Reflection of light, (a) diffused, (b) regular.
362. Mirrors.—The many purposes served by mirrors in our every-day life has made their use familiar to everyone. Yet without study and experiment few understand their properties and action. Any smooth surface may serve as a mirror, as that of glass, water, polished wood, or metal. Most objects, unlike mirrors, have irregular surfaces; these scatter or diffuse the light that falls upon them. (See Fig. 353a.) This is called diffused or irregular reflection. The reflection of light from the smooth surface of a mirror is regular. (See Fig. 353b.) In every case of reflected light, however, the angle of reflection equals the angle of incidence, diffusion being due to the irregularity of the surface. It is by means of the light "diffused" from the surface of illuminated bodies, such as plants, animals, food, and manufactured articles, that we "see" the various objects about us, and it is this light that enables us to judge of their distance, size, form, color, etc. The moon is seen by the sunlight reflected from its surface. Moonlight is therefore sunlight diffused by reflection. The new moon is that phase or condition of the moon when only a narrow strip of the moon's illuminated surface is turned toward the earth. At the time of the full moon the whole illuminated surface is seen.
363. Images Formed by a Plane Mirror.—The most common use of mirrors is in the formation of images. The way in which images are formed by a plane mirror may be illustrated by diagrams. Thus in Fig. 354, let L represent a luminous body and E and E´ two positions of the observer's eye. Take any line or ray as LO along which the light from L strikes the mirror O-O´. It will be reflected so that angle LOP equals angle POE. Similarly with any other ray, as LO´, the reflected ray O´E´ has a direction such as that angle L´O´E´ equals angle P´O´E´. Any other rays will be reflected in a similar manner, each of the reflected rays appearing to the eye to come from a point L´ behind the mirror.
Fig. 354.—The virtual image of a fixed object as seen in a plane mirror, has the same location from every position of the observer's eye.